Answers
Focus on the first column where it says "test finds student lying" since it asks "what percentage..were found to be lying". We can ignore the second column completely.
We have 282 people found to be lying based on the test (bottom of the first column). Of this total, 200 have not cheated meaning that the student isn't lying. This is based on the overall premise given at the top that states "All of them denied having cheated"
Simply divide the two values: 200/282 = 0.70921985815602 which rounds to roughly 0.7092 if you round to four decimal places
Now move the decimal over 2 spots to the right to convert to a percentage
0.7092 ---> 70.92%
Answer: 70.92%
==============================================================
Part B)
We'll use the result from part A. Subtract it from 100%
100% - 70.92% = (100 - 70.92)% = 29.08%
Answer: 29.08%
Note: another way to get this answer is to divide the values 82 over 282 to get 82/282 = 0.29078014184398 and we get the same answer roughly (after rounding)
==============================================================
Part C)
Now we focus on the second column only. We have 1718 people total and of this total, 12 have cheated. Since they initially deny cheating but they really did cheat, this is a lie they tell.
So 12/1718 = 0.0069848661234 which rounds to 0.0070 and that converts to 0.7%
Note: this isn't 7% or 70%, its point 7 percent
Answer: 0.7%
Related Questions
What is 378×6 using place value with regrouping
Answers
Analyze each product in the table.
A. Why is the first product less than 3/4?
B. Why is the second product equal to 3/4?
C. Why is the third product greater than 3/4?
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A because you are multiplying 3/4 by 1/2, you make the product smaller than 3/4
B beacue any number multiplied by one remains that number, since you are multiplying 3/4 by 1 it will remaim 3/4
C because the number multiplied by 3/4 is larger than 1 ( 3/2 = 1 1/2) the product will be larger than 3/4
Out of 25 students in mrs. Green class 19 have a pet what percent of students in mrs. Green class don't have a pet
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(We can experiment with different percentages using our trusty calculator)
30% of 25 = 7.5
We are way off, we need to bring it a bit higher if it is to reach 19. Let's try 67%
67% of 25 = 16.75
Not quite but close, lets try something a bit higher, like 76%.
76% of 25 = 19
So, 19 out of 25 is 76% all we need to do now is subtract that from 100 to get the remaining percentage.
100 - 76 = 24
24% of the students don't have a pet. :D
What number represents the most accurate estimation of 65+77
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The formula for the circumference of a circle is C=3.14 multiplied by the radius Determine the circumference when the radius r is 10 cm.
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r = 10 cm
C = 3.14 × 10 = 31.4 cm
Hope it helped!
Lisa's coffee shop makes a blend that is a mixture of two types of coffee type A coffee cost Lisa $4.50 per pound and type B coffee cost $5.50 per pound. This month's blend uses three times as many pounds of type B coffee as type A, for a total cost of $634.50. How many pounds of type a coffee were used?
Answers
The number of pounds of coffee used is 30 pounds.
Given data:
Let x be the number of pounds of type A coffee used.
Since the blend uses three times as many pounds of type B coffee as type A, the number of pounds of type B coffee used is 3x.
The cost of type A coffee is $4.50 per pound, so the cost of x pounds of type A coffee is 4.50x dollars.
The cost of type B coffee is $5.50 per pound, so the cost of 3x pounds of type B coffee is 5.50 * 3x = 16.50x dollars.
The total cost of the blend is $634.50, so the equation is:
4.50x + 16.50x = 634.50
Combine like terms:
21x = 634.50
On solving for x:
x = 634.50 / 21
x = 30
Hence, 30 pounds of type A coffee were used in the blend.
To learn more about equations, refer:
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A population has a mean of 40 and a standard deviation of 15. a sample of size 100 is taken at random from this population. the standard deviation of the sampling distribution of sample mean equals:
Answers
How many solutions does the equation have? 3+x=2–3x
Answers
3 + x = 2 - 3x
3x + x = -3 + 2
4x = -1
x = -1/4
hope this helps
IT TAKES YOU 15 MINUTES TO BIKE 5 MILES. HOW LONG DOES IT TAKE YOU TO BIKE 1 MILE
Answers
15/5 minutes : 5/5 miles .... divide both parts by 5
3 minutes : 1 mile
Answer: 3 minutes
Is 0.5 equal to 9/18
Answers
the sum of three consecutive even numbers is 42. The sum can be represented by the equation n+(n+2)+(n+4)=42. what does n represent
Answers
Then you can subtract 6 from each side
3n=36
Divide each side by 3
n=12
600 can be written as 2a x b x cd where a,b,c and d are all prime numbers find the values of a, b, c and d
Answers
[tex]600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 = 2^3 \times 3 \times 5^2[/tex]
Therefore, a = 3, b = 3, c = 5 and d = 2.
600 can be written as [tex]\(2^3 \times 3^1 \times 5^2\)[/tex], where 2, 3, and 5 are prime numbers.
To express 600 as the product of prime numbers, we'll use prime factorization.
Prime factorization involves breaking down a number into its prime factors.
Here's how we can do it:
Step 1 :**Start with the smallest prime number, 2:**
[tex]\( 600 \div 2 = 300 \)[/tex]
[tex]\( 300 \div 2 = 150 \)[/tex]
[tex]\( 150 \div 2 = 75 \)[/tex]
Step 2 :**Next, continue with the next smallest prime number, 3:**
[tex]\( 75 \div 3 = 25 \)[/tex]
[tex]\( 25 \div 5 = 5 \)[/tex]
Step 3 :**Now, we can't divide further by smaller prime numbers, so we try dividing by the next smallest prime, 5:**
[tex]\( 5 \)[/tex] is already a prime number.
Step 4 :**There are no more prime factors to consider, so we stop.**
Now, let's write down the prime factors we obtained:
[tex]\[ 600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 \][/tex]
So, [tex]\( a = 2 \), \( b = 2 \), \( c = 3 \), and \( d = 5 \).[/tex]
Therefore, we can write:
[tex]\[ 600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 \][/tex]
Thus, [tex]\( 600 \)[/tex] can be written as [tex]\( 2^3 \times 3^1 \times 5^2 \)[/tex], where [tex]\( 2, 3, \) and \( 5 \)[/tex] are all prime numbers.
Ian is 10 years old, how many candles has Ian had on all of his birthday cakes. Remember he has had 10 cakes
Answers
A coffee pot holds 2 3/4 quarts of coffee. How much is this in cups?
Answers
Add integer help just explain
Answers
Pre Calc question please help!
Answers
if half of a loaf of bread is cut into six equal slices, what fraction is each slice of the original loaf?
Answers
= 1/12
Each slice is 1/12 of the original loaf.
given: f(x)=4x^2-5
find: f(5)=
Answers
f(x) = 4x^2 - 5
f(5) = 4(5)^2 - 5
f(5) = 4(25) - 5
f(5) = 100 - 5
f(5) = 95
Hope this helps!
For what value(s) of x is g continuous? g(x) = 0 if x is rational 4x if x is irrational x is in the set of real numbers x = 4 x = −4 x = 0 none of these
Answers
Final answer:
The function g(x), being different for rational and irrational numbers, is nowhere continuous on the set of real numbers because it cannot satisfy the condition for continuity at any point.
Explanation:
We are asked to determine for what values of x the function g(x) is continuous. The function is defined to be 0 if x is rational, and 4x if x is irrational, over the set of real numbers. First, let's understand a key concept: for a function to be continuous at a point, the limit of the function as it approaches the point from either direction must be equal to the function's value at that point. In the case of g(x), the function takes the value of 0 for all rational numbers, but instantly changes to 4x for irrational numbers which are densely populated around every rational number.
Since the value of g(x) for rationals (0) is different from the nearby values for irrationals (which would be non-zero and depend on x), g(x) does not have a limit that equals its value at rational points and thus cannot be continuous at any rational number. Moreover, at irrational values of x, we cannot have continuity either, as any neighborhood around an irrational number contains rational numbers where g(x) would suddenly jump to 0, disrupting the limit process once again.
Therefore, the function g(x) is nowhere continuous on the set of real numbers since it cannot satisfy the condition for continuity at any point. Hence, the correct answer to the given question is 'none of these'.
Remove the parentheses from the following expression and combine like terms. 3(ax + b2 - c) + 2
Answers
So, it will become 3ax + 3b^2 - 3c +2. I don't think there is any like term in this expression.
Answer:
[tex]3ax+3b^2-3c+2[/tex]
Step-by-step explanation:
We have been given an expression [tex]3(ax+b^2-c)+2[/tex]. We are asked to remove the parenthesis and combine like terms for our given expression.
Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:
[tex]3*ax+3*b^2-3*c+2[/tex]
[tex]3ax+3b^2-3c+2[/tex]
We can see that our given expression don't have like terms, therefore, our expression would be [tex]3ax+3b^2-3c+2[/tex].
The total area of this shape is 44 square inches. The area of the triangle is 20 square inches. Write and solve an equation to find the area of the rectangle
Answers
Answer:
The equation is: x + 20 = 44
The area of the rectangle is 24 inches.
Step-by-step explanation:
The total area of the shape is 44 square inches.
The area of the triangle is 20 square inches.
We need to find the area of the rectangle.
Total area = Area of the triangle + Area of the rectangle.
Let "x" be the area of the rectangle.
So the equation is
44 = 20 + x
This can be written as x + 20 = 44
Now let's find the value fo x.
Subtract 20 from both sides, we get
x + 20 - 20 = 44 - 20
x = 24 square inches.
Therefore, the area of the rectangle is 24 inches.
I have 140 markers. how many boxes of 10 markers does I need to get 180 markers
Answers
Which expression results when the change of base formula is applied to log4(x+2) ?
Answers
So it would be log(x+2)/log4.
The answer is the first one.
Answer:
Option A : [tex]\frac{log(x+2)}{log(4)}[/tex]
Step-by-step explanation:
Write the expression when the change of base formula is applied to log4(x+2
Given [tex]log_4(x+2)[/tex]
USe change of base formula
[tex]log_b(a)= \frac{log(a)}{log(b)}[/tex]
WE apply change of base formula for the given log
the base of log becomes the denominator .
Numerator becomes the x+2
[tex]log_4(x+2)= \frac{log(x+2)}{log(4)}[/tex]
option A is the correct answer
How are the numbers 579 and 597 different
Answers
597 is a greater value than 579.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
Rounding some number to a specific value is making its value simpler mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We have to find How are the numbers 579 and 597 different to each other.
As we can see that the last two digit of the numbers 79 and 97 are flipped.
We know that 97 is greater than 79.
Therefore, 597 is a greater value than 579.
Learn more about a number pattern:
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which values are equivalent to the fraction below 3^6/3^8
Answers
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 212 h. Train B reaches station B after 4 h. Station A and Station B are 585 mi apart. What is the rate of the trains?
Answers
so, keeping in mind that both trains are going at the same speed, say speed of "r" mph, after 212 hours A arrived at station A and after 4 hours, B arrived at station B.
now, the distance covered by train A is say "d", we know both stations are 585 miles apart, so, if train A covered "d" miles in those 212 hours, then train B covered the slack from 585 and d, that is "585 - d".
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Train A}&d&r&212\\ \textit{Train B}&585 - d&r&4 \end{array} \\\\\\ \begin{cases} \boxed{d}=212r\\ 585-d=4r\\ ----------\\ 585-\boxed{212r}=4r \end{cases} \\\\\\ 585=216r\implies \cfrac{585}{216}=r\implies \cfrac{65}{24}=r\implies \stackrel{mph}{2\frac{17}{24}}=r[/tex]
I just had the same question on a test and the answer was 90 MPH. Hope this helps somebody!
Liem is 6 feet 2 inches, Eli is 5 feet 9 inches, Faith is 6 feet, and Simon is 5 feet 4 inches. In yards, what is the total of their heights?
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need help with this
Answers
(450-210)/4+50=110
hope this helps
After that he divided the money (240/4=60) which gives him $60, then he distributed 3 (60-30=20 or 60/3=20).
he then finds $50 on the road (50+20=70) which he now has $70.
The answer is $70
How much greater is 98×50 than 97×50 with actual calculating it
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Use distributive property and mental math to find the product
7x49
Answers
2 ways we can do this is to write 49 as either 40+9 or 50-1
if we do 40+9
7(49)=7(40+9)=7(40)+7(9)=280+63=343
if we do 50-1
7(49)=7(50-1)=7(50)+7(-1)=350-7=343